I'm coding a jQuery plugin that basically checks if a set of checkboxes groups have at least x options checked. A checkbox group is named as name=group[]. You'd call the plugin like:

$(':checkbox').checkpass({min: 1}) // Make sure at least one checkbox per group is checked

I've been working on this piece of code for a couple days trying to make it as short and fast as possible because I'm going to implement this on a very large form.
Is it possible to make it shorter/faster or I reached the limit? You can check live example at http://jsfiddle.net/elclanrs/GFCKA/. And here's the code:

(function($) {
    $.fn.checkpass = function(options) {

        var opt = $.extend({
            min: function() {
                return (min === 'undefined') ? 1 : min;
            },
            errorContainer: '<ul class="checkpass-errors">',
            errorWrap: '<li class="error">'
        }, options);

        var $ckboxes = this,
            names = [],
            num = 0,
            $errors = $(opt.errorContainer);

        $ckboxes.each(function() {
            var name = this.name;
            if (!~$.inArray(name, names)) {
                names.push(name);
            }
        });

        for (var i = 0, l = names.length; i < l; i++) {
            $checked = $ckboxes.filter('[name="' + names[i] + '"]:checked');
            if ($checked[opt.min - 1]) {
                num++;
            } else {
                if (opt.min > 0) {
                    var $err = $(opt.errorWrap),
                        _remaining = opt.min - $checked.length,
                        _name = names[i].match(/\w+/).toString()
                                .replace(/^\w/, function($0) {
                                    return $0.toUpperCase();
                                });
                    $err.html('<strong>' + _name +
                              ':</strong> Check ' +
                              _remaining + ' more.').appendTo($errors);
                }
            }
        }

        return {
            isValid: !! (num === names.length),
            errors: $errors
        };
    };
})(jQuery);